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## Getting to the Root of Things

Take a number, such as 25. Now subtract the odds in sequence:

25 - 1 = 24
24 - 3 = 21
21 - 5 = 16
16 - 7 = 9
9 - 9 = 0 [Stop]

It took five subtractions to reach zero, thus the square root of 25 is 5.

Check....does this process work with 16? 9? 225? etc.

Task #1: Show visually why this process works.

Task #2:Can you adjust the process for numbers that are not perfect squares? For example, can you use it (in modified form) to find the square root of 21?

Hint: Draw a five by five square of dots to represent the number 25. Then...

Solution Commentary: Look up what a gnomen is....and how it relates to a carpenter's square.

In the 5 x 5 square of dots, remove 1 dot (i.e. upper left hand corner dot).

Now, remove 3 dots in the shape of a carpenter's square or gnomen...continue with 5 dots, etc.

Do you think this process implies that every square is the sum of consecutive odds? Can you prove it?